* Euro zone country narrowly avoided international bailout
* Son of Olympic athlete wins, must lead recovery
* PM frontrunner cool on some privatisations
* Investors wary of backsliding (Updates with official count)
By Marja Novak and Zoran Radosavljevic
LJUBLJANA, July 13 (Reuters) - Centre-left political novice Miro Cerar led his party to victory in Slovenia's election on Sunday, indicating he would rewrite a reform package agreed with the European Union to fix the euro zone member's depleted finances.
The result will test investor nerves, given Cerar's hostility to some of the big-ticket privatisations that the EU says are key to a long-term fix for Slovenia, which narrowly avoided having to seek an international bailout for its banks last year.
Cerar's six-week-old SMC party won 34.8 percent of the vote, which translates to 36 seats in the 90-seat parliament. That would give the 50-year-old law professor the strong mandate his recent predecessors have lacked, potentially going some way to restoring political stability after years of turbulence and weak government.
The centre-right SDS party was in second place with 20.6 percent and a string of smaller centre-left parties also won seats and were lining up to join Cerar in government.
Success for Cerar, whose Olympic gymnast father was one of Slovenia's greatest ever sportsmen, is punishment by voters for the traditional parties, tarnished by corruption scandals and years of economic turmoil in the ex-Yugoslav republic.
Outgoing Prime Minister Alenka Bratusek called Sunday's snap election after losing public confidence. Cerar's government will now oversee a raft of crisis measures agreed with the EU to reduce Slovenia's budget deficit and remake an economy heavily controlled by the state.
Cerar, however, opposes the sale of telecoms provider Telekom Slovenia and the international airport, Aerodrom Ljubljana, fuelling investor fears of backsliding.
Suggesting he planned to revisit the crisis programme agreed under the previous government, Cerar told Reuters: "Our party will aim for Slovenia to fulfil its EU obligations but within that we will seek our own ways to reach these goals in the best way for Slovenia."
He said his cabinet would immediately consider which companies would remain in state hands and what to do with the rest. "I'll do my best to have our privatisation programme in place this year," he said. "This will be one of the priorities of the government."
The outgoing government suspended the privatisation process this month pending the formation of a new government, which is not expected before mid-September.
Cerar will have to find other ways to raise cash if he is to meet a target agreed with the EU to slash back Slovenia's budget deficit to 3 percent of output by 2015, from a forecast 4.2 percent this year.
He will form the fourth government since the 2008 financial crisis, which shredded Slovenia's reputation as an economic trailblazer in ex-Communist Eastern Europe.
Analysts expect him to turn to the Social Democrats (SD) and the Desus pensioners' party to form a coalition, but he may cast the net even wider in order to shore up support.
Both the SD and Desus were part of the outgoing cabinet and were reluctant recruits to the toughest of Bratusek's crisis measures, particularly privatisation.
"In the more likely scenario that the centre-left assumes power, the next cabinet will likely delay or halt many of the reforms necessary to improve Slovenia's public finances," said Tsveta Petrova, an analyst at Eurasia group.
"Still, the country might see some anti-corruption initiatives in line with Cerar's election campaign."
Cerar created his Party of Miro Cerar (SMC) barely six weeks ago and shot to the top of opinion polls among voters looking for someone new and untarnished by the corruption scandals that have dogged the mainstream parties.
He owes much of his celebrity to his gymnast father, twice Olympic pommel horse champion when Slovenia was part of Yugoslavia.
State meddling in the economy was at the heart of the crisis that began when the global economic downturn hit Slovenia's vital exports. Bad loans exposed years of reckless lending and an economic model that had largely avoided the privatisations pursued by others in Eastern Europe after the Cold War ended.
In December 2013, Bratusek's government poured 3.3 billion euros into the banking system to keep it afloat and avoided becoming the latest member of the 17-nation euro zone to seek a bailout from the European Union and International Monetary Fund. (Writing by Matt Robinson; Editing by Susan Fenton)